Riemann-Hilbert analysis for a Nikishin system Articles uri icon

publication date

  • July 2018

start page

  • 1019

end page

  • 1050

issue

  • 7

volume

  • 209

international standard serial number (ISSN)

  • 1064-5616

electronic international standard serial number (EISSN)

  • 1468-4802

abstract

  • In this paper we give the asymptotic behaviour of type I multiple orthogonal polynomials for a Nikishin system of order two with two disjoint intervals. We use the Riemann-Hilbert problem for multiple orthogonal polynomials and steepest descent analysis for oscillatory Riemann-Hilbert problems to obtain the asymptotic behaviour in all the relevant regions of the complex plane.

keywords

  • multiple orthogonal polynomials; Riemann-Hilbert problem; Hermite-Pade approximations; asymptotic